TSTP Solution File: GRA004+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:43:18 EDT 2024
% Result : Theorem 0.83s 0.80s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 122 ( 8 unt; 0 def)
% Number of atoms : 491 ( 106 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 593 ( 224 ~; 208 |; 120 &)
% ( 17 <=>; 21 =>; 0 <=; 3 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 13 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 291 ( 253 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1464,plain,
$false,
inference(avatar_sat_refutation,[],[f156,f161,f248,f270,f298,f337,f539,f994,f1011,f1083,f1163,f1248,f1462]) ).
fof(f1462,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f1461]) ).
fof(f1461,plain,
( $false
| ~ spl13_3 ),
inference(trivial_inequality_removal,[],[f1460]) ).
fof(f1460,plain,
( tail_of(sK2) != tail_of(sK2)
| ~ spl13_3 ),
inference(equality_resolution,[],[f1279]) ).
fof(f1279,plain,
( ! [X0] :
( head_of(X0) != head_of(sK2)
| tail_of(X0) != tail_of(sK2) )
| ~ spl13_3 ),
inference(backward_demodulation,[],[f1198,f155]) ).
fof(f155,plain,
( head_of(sK2) = head_of(sK3)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f153,plain,
( spl13_3
<=> head_of(sK2) = head_of(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f1198,plain,
! [X0] :
( tail_of(X0) != tail_of(sK2)
| head_of(X0) != head_of(sK3) ),
inference(resolution,[],[f87,f293]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ precedes(X0,X2,sK4)
| tail_of(X0) != tail_of(X1)
| head_of(X2) != head_of(X1) ),
inference(resolution,[],[f90,f86]) ).
fof(f86,plain,
shortest_path(sK0,sK1,sK4),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( ( head_of(sK2) = head_of(sK3)
| head_of(sK3) = tail_of(sK2)
| ( head_of(sK3) = head_of(sK5)
& tail_of(sK2) = tail_of(sK5) ) )
& precedes(sK2,sK3,sK4)
& shortest_path(sK0,sK1,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f39,f62,f61]) ).
fof(f61,plain,
( ? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| head_of(X3) = tail_of(X2)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ( head_of(sK2) = head_of(sK3)
| head_of(sK3) = tail_of(sK2)
| ? [X5] :
( head_of(X5) = head_of(sK3)
& tail_of(X5) = tail_of(sK2) ) )
& precedes(sK2,sK3,sK4)
& shortest_path(sK0,sK1,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X5] :
( head_of(X5) = head_of(sK3)
& tail_of(X5) = tail_of(sK2) )
=> ( head_of(sK3) = head_of(sK5)
& tail_of(sK2) = tail_of(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| head_of(X3) = tail_of(X2)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
? [X0,X1,X2,X3,X4] :
( ( head_of(X2) = head_of(X3)
| head_of(X3) = tail_of(X2)
| ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( head_of(X2) != head_of(X3)
& head_of(X3) != tail_of(X2)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( head_of(X6) != head_of(X7)
& tail_of(X6) != head_of(X7)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',shortest_path_properties_lemma) ).
fof(f90,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ shortest_path(X0,X1,X4)
| tail_of(X2) != tail_of(X5)
| ~ precedes(X2,X3,X4)
| head_of(X3) != head_of(X5) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',shortest_path_properties) ).
fof(f87,plain,
precedes(sK2,sK3,sK4),
inference(cnf_transformation,[],[f63]) ).
fof(f1248,plain,
~ spl13_109,
inference(avatar_contradiction_clause,[],[f1245]) ).
fof(f1245,plain,
( $false
| ~ spl13_109 ),
inference(resolution,[],[f1082,f87]) ).
fof(f1082,plain,
( ! [X0] : ~ precedes(X0,sK3,sK4)
| ~ spl13_109 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1081,plain,
( spl13_109
<=> ! [X0] : ~ precedes(X0,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).
fof(f1163,plain,
~ spl13_97,
inference(avatar_contradiction_clause,[],[f1162]) ).
fof(f1162,plain,
( $false
| ~ spl13_97 ),
inference(subsumption_resolution,[],[f1088,f184]) ).
fof(f184,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK4)
| ~ precedes(X1,X0,sK4) ),
inference(resolution,[],[f91,f86]) ).
fof(f91,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f41]) ).
fof(f1088,plain,
( precedes(sK2,sK2,sK4)
| ~ spl13_97 ),
inference(backward_demodulation,[],[f87,f1010]) ).
fof(f1010,plain,
( sK2 = sK3
| ~ spl13_97 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f1008,plain,
( spl13_97
<=> sK2 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_97])]) ).
fof(f1083,plain,
( spl13_12
| spl13_109
| ~ spl13_22
| ~ spl13_96 ),
inference(avatar_split_clause,[],[f1078,f1004,f335,f1081,f250]) ).
fof(f250,plain,
( spl13_12
<=> ! [X0,X1] : ~ path(X0,X1,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f335,plain,
( spl13_22
<=> ! [X0] :
( precedes(X0,sK3,sK4)
| ~ on_path(X0,sK4)
| ~ sequential(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f1004,plain,
( spl13_96
<=> sequential(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_96])]) ).
fof(f1078,plain,
( ! [X2,X0,X1] :
( ~ precedes(X0,sK3,sK4)
| ~ path(X1,X2,sK4) )
| ~ spl13_22
| ~ spl13_96 ),
inference(resolution,[],[f1028,f93]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK6(X0,X3,X4),X4,X0)
& sequential(X3,sK6(X0,X3,X4)) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f66,f67]) ).
fof(f67,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK6(X0,X3,X4),X4,X0)
& sequential(X3,sK6(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',precedes_properties) ).
fof(f1028,plain,
( ~ on_path(sK3,sK4)
| ~ spl13_22
| ~ spl13_96 ),
inference(subsumption_resolution,[],[f1023,f184]) ).
fof(f1023,plain,
( ~ on_path(sK3,sK4)
| precedes(sK3,sK3,sK4)
| ~ spl13_22
| ~ spl13_96 ),
inference(resolution,[],[f1006,f336]) ).
fof(f336,plain,
( ! [X0] :
( ~ sequential(X0,sK2)
| ~ on_path(X0,sK4)
| precedes(X0,sK3,sK4) )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f1006,plain,
( sequential(sK3,sK2)
| ~ spl13_96 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f1011,plain,
( spl13_96
| spl13_97
| ~ spl13_17
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f505,f268,f280,f1008,f1004]) ).
fof(f280,plain,
( spl13_17
<=> edge(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f268,plain,
( spl13_16
<=> ! [X0] :
( head_of(X0) != head_of(sK3)
| ~ edge(X0)
| sK2 = X0
| sequential(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f505,plain,
( ~ edge(sK3)
| sK2 = sK3
| sequential(sK3,sK2)
| ~ spl13_16 ),
inference(equality_resolution,[],[f269]) ).
fof(f269,plain,
( ! [X0] :
( head_of(X0) != head_of(sK3)
| ~ edge(X0)
| sK2 = X0
| sequential(X0,sK2) )
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f994,plain,
( spl13_12
| spl13_12
| spl13_17 ),
inference(avatar_split_clause,[],[f991,f280,f250,f250]) ).
fof(f991,plain,
( ! [X2,X3,X0,X1] :
( ~ path(X0,X1,sK4)
| ~ path(X2,X3,sK4) )
| spl13_17 ),
inference(resolution,[],[f566,f87]) ).
fof(f566,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X3,sK3,X2)
| ~ path(X0,X1,X2)
| ~ path(X4,X5,X2) )
| spl13_17 ),
inference(resolution,[],[f181,f282]) ).
fof(f282,plain,
( ~ edge(sK3)
| spl13_17 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( edge(X1)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2)
| ~ path(X5,X6,X2) ),
inference(resolution,[],[f93,f111]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| edge(X3)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X3,X0] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',on_path_properties) ).
fof(f539,plain,
( ~ spl13_1
| ~ spl13_4 ),
inference(avatar_contradiction_clause,[],[f538]) ).
fof(f538,plain,
( $false
| ~ spl13_1
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f537,f160]) ).
fof(f160,plain,
( tail_of(sK2) = tail_of(sK5)
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f158,plain,
( spl13_4
<=> tail_of(sK2) = tail_of(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f537,plain,
( tail_of(sK2) != tail_of(sK5)
| ~ spl13_1 ),
inference(trivial_inequality_removal,[],[f535]) ).
fof(f535,plain,
( head_of(sK3) != head_of(sK3)
| tail_of(sK2) != tail_of(sK5)
| ~ spl13_1 ),
inference(superposition,[],[f507,f147]) ).
fof(f147,plain,
( head_of(sK3) = head_of(sK5)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f145,plain,
( spl13_1
<=> head_of(sK3) = head_of(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f507,plain,
! [X0] :
( head_of(X0) != head_of(sK3)
| tail_of(X0) != tail_of(sK2) ),
inference(resolution,[],[f293,f87]) ).
fof(f337,plain,
( spl13_12
| spl13_22 ),
inference(avatar_split_clause,[],[f333,f335,f250]) ).
fof(f333,plain,
! [X2,X0,X1] :
( precedes(X0,sK3,sK4)
| ~ sequential(X0,sK2)
| ~ on_path(X0,sK4)
| ~ path(X1,X2,sK4) ),
inference(resolution,[],[f162,f87]) ).
fof(f162,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X5,X4,X0)
| precedes(X3,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(subsumption_resolution,[],[f98,f93]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4,X5] :
( precedes(X3,X4,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3)
& on_path(X6,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',precedes_defn) ).
fof(f298,plain,
~ spl13_12,
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f297,plain,
( $false
| ~ spl13_12 ),
inference(resolution,[],[f295,f86]) ).
fof(f295,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK4)
| ~ spl13_12 ),
inference(resolution,[],[f251,f99]) ).
fof(f99,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
& path(X0,X1,sK7(X0,X1,X2)) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f71,f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2)))
& path(X0,X1,sK7(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',shortest_path_defn) ).
fof(f251,plain,
( ! [X0,X1] : ~ path(X0,X1,sK4)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f270,plain,
( ~ spl13_5
| spl13_16
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f213,f149,f268,f166]) ).
fof(f166,plain,
( spl13_5
<=> edge(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f149,plain,
( spl13_2
<=> head_of(sK3) = tail_of(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f213,plain,
( ! [X0] :
( head_of(X0) != head_of(sK3)
| sequential(X0,sK2)
| sK2 = X0
| ~ edge(sK2)
| ~ edge(X0) )
| ~ spl13_2 ),
inference(superposition,[],[f119,f151]) ).
fof(f151,plain,
( head_of(sK3) = tail_of(sK2)
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f119,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| sequential(X0,X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196',sequential_defn) ).
fof(f248,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f247,plain,
( $false
| spl13_5 ),
inference(resolution,[],[f245,f86]) ).
fof(f245,plain,
( ! [X0,X1] : ~ shortest_path(X0,X1,sK4)
| spl13_5 ),
inference(resolution,[],[f244,f99]) ).
fof(f244,plain,
( ! [X0,X1] : ~ path(X0,X1,sK4)
| spl13_5 ),
inference(subsumption_resolution,[],[f243,f175]) ).
fof(f175,plain,
( ! [X0] : ~ sequential(sK2,X0)
| spl13_5 ),
inference(resolution,[],[f168,f115]) ).
fof(f115,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f168,plain,
( ~ edge(sK2)
| spl13_5 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f243,plain,
( ! [X0,X1] :
( sequential(sK2,sK6(sK4,sK2,sK3))
| ~ path(X0,X1,sK4) )
| spl13_5 ),
inference(subsumption_resolution,[],[f242,f175]) ).
fof(f242,plain,
! [X0,X1] :
( sequential(sK2,sK3)
| sequential(sK2,sK6(sK4,sK2,sK3))
| ~ path(X0,X1,sK4) ),
inference(resolution,[],[f94,f87]) ).
fof(f94,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sequential(X3,X4)
| sequential(X3,sK6(X0,X3,X4))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f161,plain,
( spl13_4
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f88,f153,f149,f158]) ).
fof(f88,plain,
( head_of(sK2) = head_of(sK3)
| head_of(sK3) = tail_of(sK2)
| tail_of(sK2) = tail_of(sK5) ),
inference(cnf_transformation,[],[f63]) ).
fof(f156,plain,
( spl13_1
| spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f89,f153,f149,f145]) ).
fof(f89,plain,
( head_of(sK2) = head_of(sK3)
| head_of(sK3) = tail_of(sK2)
| head_of(sK3) = head_of(sK5) ),
inference(cnf_transformation,[],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.09/0.30 % Computer : n024.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri May 3 18:26:07 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.30 This is a FOF_THM_RFO_SEQ problem
% 0.09/0.30 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.ZXKvqzYM5r/Vampire---4.8_11196
% 0.15/0.76 % (11310)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.15/0.76 % (11312)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.15/0.76 % (11311)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.15/0.76 % (11315)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.15/0.76 % (11313)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.15/0.76 % (11317)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.15/0.76 % (11314)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.15/0.76 % (11316)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.15/0.76 % (11317)Refutation not found, incomplete strategy% (11317)------------------------------
% 0.15/0.76 % (11317)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.76 % (11317)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.76
% 0.15/0.76 % (11317)Memory used [KB]: 1049
% 0.15/0.76 % (11317)Time elapsed: 0.002 s
% 0.15/0.76 % (11317)Instructions burned: 2 (million)
% 0.15/0.76 % (11315)Refutation not found, incomplete strategy% (11315)------------------------------
% 0.15/0.76 % (11315)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.76 % (11315)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.76
% 0.15/0.76 % (11315)Memory used [KB]: 1053
% 0.15/0.76 % (11315)Time elapsed: 0.003 s
% 0.15/0.76 % (11315)Instructions burned: 3 (million)
% 0.15/0.76 % (11313)Refutation not found, incomplete strategy% (11313)------------------------------
% 0.15/0.76 % (11313)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.76 % (11317)------------------------------
% 0.15/0.76 % (11317)------------------------------
% 0.15/0.76 % (11313)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.76
% 0.15/0.76 % (11313)Memory used [KB]: 1049
% 0.15/0.76 % (11313)Time elapsed: 0.003 s
% 0.15/0.76 % (11313)Instructions burned: 3 (million)
% 0.15/0.76 % (11315)------------------------------
% 0.15/0.76 % (11315)------------------------------
% 0.15/0.76 % (11313)------------------------------
% 0.15/0.76 % (11313)------------------------------
% 0.15/0.77 % (11320)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.15/0.77 % (11319)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.15/0.77 % (11318)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.15/0.77 % (11318)Refutation not found, incomplete strategy% (11318)------------------------------
% 0.15/0.77 % (11318)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.77 % (11318)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.77
% 0.15/0.77 % (11318)Memory used [KB]: 1135
% 0.15/0.77 % (11318)Time elapsed: 0.005 s
% 0.15/0.77 % (11318)Instructions burned: 7 (million)
% 0.15/0.77 % (11318)------------------------------
% 0.15/0.77 % (11318)------------------------------
% 0.15/0.77 % (11321)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.15/0.78 % (11310)Instruction limit reached!
% 0.15/0.78 % (11310)------------------------------
% 0.15/0.78 % (11310)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.78 % (11310)Termination reason: Unknown
% 0.15/0.78 % (11310)Termination phase: Saturation
% 0.15/0.78
% 0.15/0.78 % (11310)Memory used [KB]: 1346
% 0.15/0.78 % (11310)Time elapsed: 0.018 s
% 0.15/0.78 % (11310)Instructions burned: 36 (million)
% 0.15/0.78 % (11310)------------------------------
% 0.15/0.78 % (11310)------------------------------
% 0.15/0.78 % (11314)Instruction limit reached!
% 0.15/0.78 % (11314)------------------------------
% 0.15/0.78 % (11314)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.78 % (11314)Termination reason: Unknown
% 0.15/0.78 % (11314)Termination phase: Saturation
% 0.15/0.78
% 0.15/0.78 % (11314)Memory used [KB]: 1411
% 0.15/0.78 % (11314)Time elapsed: 0.019 s
% 0.15/0.78 % (11314)Instructions burned: 34 (million)
% 0.15/0.78 % (11314)------------------------------
% 0.15/0.78 % (11314)------------------------------
% 0.15/0.78 % (11322)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.15/0.78 % (11323)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.15/0.79 % (11311)Instruction limit reached!
% 0.15/0.79 % (11311)------------------------------
% 0.15/0.79 % (11311)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.79 % (11311)Termination reason: Unknown
% 0.15/0.79 % (11311)Termination phase: Saturation
% 0.15/0.79
% 0.15/0.79 % (11311)Memory used [KB]: 1714
% 0.15/0.79 % (11311)Time elapsed: 0.030 s
% 0.15/0.79 % (11311)Instructions burned: 51 (million)
% 0.15/0.79 % (11311)------------------------------
% 0.15/0.79 % (11311)------------------------------
% 0.15/0.79 % (11324)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.15/0.80 % (11321)Instruction limit reached!
% 0.15/0.80 % (11321)------------------------------
% 0.15/0.80 % (11321)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.80 % (11321)Termination reason: Unknown
% 0.15/0.80 % (11321)Termination phase: Saturation
% 0.15/0.80
% 0.15/0.80 % (11321)Memory used [KB]: 1794
% 0.15/0.80 % (11321)Time elapsed: 0.028 s
% 0.15/0.80 % (11321)Instructions burned: 53 (million)
% 0.15/0.80 % (11321)------------------------------
% 0.15/0.80 % (11321)------------------------------
% 0.15/0.80 % (11312)First to succeed.
% 0.83/0.80 % (11316)Instruction limit reached!
% 0.83/0.80 % (11316)------------------------------
% 0.83/0.80 % (11316)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.83/0.80 % (11316)Termination reason: Unknown
% 0.83/0.80 % (11325)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.83/0.80 % (11316)Termination phase: Saturation
% 0.83/0.80
% 0.83/0.80 % (11316)Memory used [KB]: 1930
% 0.83/0.80 % (11316)Time elapsed: 0.044 s
% 0.83/0.80 % (11316)Instructions burned: 84 (million)
% 0.83/0.80 % (11316)------------------------------
% 0.83/0.80 % (11316)------------------------------
% 0.83/0.80 % (11312)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11306"
% 0.83/0.80 % (11312)Refutation found. Thanks to Tanya!
% 0.83/0.80 % SZS status Theorem for Vampire---4
% 0.83/0.80 % SZS output start Proof for Vampire---4
% See solution above
% 0.83/0.80 % (11312)------------------------------
% 0.83/0.80 % (11312)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.83/0.80 % (11312)Termination reason: Refutation
% 0.83/0.80
% 0.83/0.80 % (11312)Memory used [KB]: 1723
% 0.83/0.80 % (11312)Time elapsed: 0.044 s
% 0.83/0.80 % (11312)Instructions burned: 79 (million)
% 0.83/0.80 % (11306)Success in time 0.488 s
% 0.83/0.81 % Vampire---4.8 exiting
%------------------------------------------------------------------------------